FLUCTUATION THEORY OF SOLUTIONS Applications in Chemistry, Chemical Engineering, and Biophysics E D I T E D Paul E Smith ■ B Y Enrico Matteoli ■ John P O’Connell Fluctuation theory oF SolutionS Applications in Chemistry, Chemical Engineering, and Biophysics CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2013 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20130118 International Standard Book Number-13: 978-1-4398-9923-6 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this 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CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com FLUCTUATION THEORY OF SOLUTIONS Applications in Chemistry, Chemical Engineering, and Biophysics E D I T E D Paul E Smith ■ B Y Enrico Matteoli ■ John P O’Connell Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business Contents Preface vii Acknowledgments ix Contributor List xi Prolegomenon to the Fluctuation Theory of Solutions xiii Robert M Mazo Chapter Fluctuation Solution Theory: A Primer .1 Paul E Smith, Enrico Matteoli, and John P O’Connell Chapter Global and Local Properties of Mixtures: An Expanded Paradigm for the Study of Mixtures 35 Arieh Ben-­Naim Chapter Preferential Solvation in Mixed Solvents 65 Yizhak Marcus Chapter Kirkwood–Buff Integrals in Fully Miscible Ternary Systems: Thermodynamic Data, Calculation, Representation, and Interpretation 93 Enrico Matteoli, Paolo Gianni, and Luciano Lepori Chapter Accurate Force Fields for Molecular Simulation 117 Elizabeth A Ploetz, Samantha Weerasinghe, Myungshim Kang, and Paul E Smith Chapter Fluctuation Solution Theory Properties from Molecular Simulation 133 Jens Abildskov, Rasmus Wedberg, and John P O’Connell Chapter Concentration Fluctuations and Microheterogeneity in Aqueous Mixtures: New Developments in Analogy with Microemulsions 163 Aurélien Perera v vi Contents Chapter Solvation Phenomena in Dilute Solutions: Formal Results, Experimental Evidence, and Modeling Implications 191 Ariel A Chialvo Chapter Molecular Thermodynamic Modeling of Fluctuation Solution Theory Properties 225 John P O’Connell and Jens Abildskov Chapter 10 Solubilities of Various Solutes in Multiple Solvents: A Fluctuation Theory Approach 257 Ivan L Shulgin and Eli Ruckenstein Chapter 11 Why Is Fluctuation Solution Theory Indispensable for the Study of Biomolecules? 287 Seishi Shimizu Chapter 12 Osmophobics and Hydrophobics: The Changing Landscape of Protein Folding 309 Matthew Auton and B Montgomery Pettitt References 325 Preface Many, if not most, processes of interest occur in solutions It is therefore somewhat unfortunate that our understanding of solutions and their properties remains rather limited There are essentially two theories of solutions that can be considered exact These are the McMillan–Mayer theory of solutions and Fluctuation Solution Theory (FST), or the Kirkwood–Buff (KB) theory of solutions The former has practical issues, which limit most applications to solutes at low concentrations The latter has no such issues Nevertheless, the general acceptance and appreciation of FST remains limited It is the intention of this book to outline and promote the considerable advantages of using FST/­K B theory to study a wide range of solution properties Fluctuation solution theory is an exact theory that can be applied to any stable solution containing any number of components at any concentration involving any type of molecules of any size The theory is primarily used to relate thermodynamic properties of solutions to the underlying molecular distributions, and vice versa This collection has been developed to outline the general concepts and theoretical basis of FST, and to provide a range of applications relevant to the areas of chemistry, chemical engineering, and biophysics, as described by experts in each field It serves as an update to a previous compilation published over two decades ago (Matteoli and Mansoori 1990) Many substantial advances have been made since the previous compilation was published, and these are included in the present edition In particular, the application of FST to study biological systems is now well established and promises to be even more fruitful in the near future In addition, continuing developments in computer simulation hardware and software have increased the range of potential applications, helping to improve our understanding of solution properties, and providing access to the required integrals that form the basis of the theory This book includes a historical perspective (Prolegomenon) and an introductory section (Chapter 1) outlining the basic theory, including the underlying concepts and a basic derivation that is aimed at the casual reader Additional chapters then provide applications of FST to help rationalize and understand simple model (Chapter  2), binary (Chapter 3), and ternary (Chapter 4) systems with a focus on their thermodynamic properties and the concept of preferential solvation The use of FST to help develop more accurate potential functions for simulation is illustrated (Chapter 5), followed by a detailed outline of the problems and possible solutions for determining the integrals over molecular distribution functions from simulation as required by the theory (Chapter 6) New approaches to help understand microheterogeneities in solutions are then described (Chapter 7), together with an overview of solvation in real and model systems including systems under critical conditions (Chapter 8) The use of FST to describe and model solute solubility in a variety of systems is then discussed (Chapters and 10) Finally, a series of biological applications are provided which illustrate the use of FST to the study of cosolvent effects on proteins (Chapter 11), and the implications for protein folding (Chapter 12) Where possible, vii viii Preface we have attempted to maintain the same notation (established in Chapter 1) and a set of symbol descriptions is provided for reference However, the number of possible applications of FST extends beyond those presented here Indeed, there are many additional applications that deserve attention, but have not been included due to either space limitations, or because they represent newly emerging areas, which are not yet fully mature A reasonably comprehensive list of the currently available applications of FST includes: thermodynamic properties of binary and ternary solutions; transfer free energies; osmotic systems; solute solubility and Henry’s constant (including critical regions); descriptions of preferential solvation; preferential interactions in biological systems including osmotic stress and volumetric studies; density fluctuations provided by light scattering; evaluation of force fields for computer simulations; chemical equilibria, and the effects of pressure and composition on molecular crowding and protein denaturation; and the effects of cosolvents on surface tension, crystal morphology, and micelle formation More recently, one has also been able to move beyond isothermal conditions, which provide molecular level interpretations of additional thermodynamic quantities It is hoped that the efforts described here help to convey the beauty and simplicity of FST to a range of researchers in a variety of fields We are confident that FST provides the most rigorous and useful approach for understanding and rationalizing a wide range of solution properties, especially when used in conjunction with computer simulation data Paul E Smith Enrico Matteoli John P O’Connell References 341 Lupis, C H P 1983 Chemical Thermodynamics of Materials New York: North-­Holland Mackerell, A D 2004 Empirical force fields for biological macromolecules: Overview and issues Journal of Computational Chemistry 25, 1584 Mackerell, A D., D Bashford, M Bellott, R L Dunbrack, J D Evanseck, M J Field, S Fischer, J Gao, H Guo, S Ha, D J McCarthy, L Kuchnir, K Kuczera, F T K Lau, C Mattos, S Michnick, T Ngo, D T Nguyen, B Prodhom, W E Reiher, B Roux, M Schlenkrich, J C Smith, R Stote, J Straub, M Watanabe, J Wiorkiewicz-­Kuczera, D Yin, and M Karplus 1998 All-­atom empirical potential for molecular modeling and dynamics studies of proteins Journal of Physical 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applications of the CHARMM force fields Wiley Interdisciplinary Reviews-­Computational Molecular Science 2, 167 Zielkiewicz, J 1995a Kirkwood–Buff integrals in the binary and ternary mixtures containing heptane and aliphatic alcohol Journal of Physical Chemistry 99, 3357 Zielkiewicz, J 1995b Solvation of DMF in the N,N-­dimethylformamide + alcohol + water mixtures investigated by means of the Kirkwood–Buff integrals Journal of Physical Chemistry 99, 4787 Zoranić, L., R Mazighi, F Sokolić, and A Perera 2009 Concentration fluctuations and microheterogeneity in aqueous amide mixtures Journal of Chemical Physics 130, 124315 Zou, Q., B J Bennion, V Daggett, and K P Murphy 2002 The molecular mechanism of stabilization of proteins by TMAO and its ability to counteract the effects of urea Journal of the American Chemical Society 124, 1192 CHEMICAL ENGINEERING There are essentially two theories of solutions that can be considered exact: the McMillan–Mayer theory and Fluctuation Solution Theory (FST) The first is mostly limited to solutes at low concentrations, while FST has no such issue It is an exact theory that can be applied to any stable solution regardless of the number of components and their concentrations, and the types of molecules and their sizes Fluctuation Theory of Solutions: Applications in Chemistry, Chemical Engineering, and Biophysics outlines the general concepts and theoretical basis of FST and provides a range of applications described by experts in chemistry, chemical engineering, and biophysics The book, which begins with a historical perspective and an introductory chapter, includes a basic derivation for more casual readers It is then devoted to providing new and very recent applications of FST The first application chapters focus on simple model, binary, and ternary systems, using FST to explain their thermodynamic properties and the concept of preferential solvation Later chapters illustrate the use of FST to develop more accurate potential functions for simulation, describe new approaches to elucidate microheterogeneities in solutions, and present an overview of solvation in new and model systems, including those under critical conditions Expert contributors also discuss the use of FST to model solute solubility in a variety of systems The final chapters present a series of biological applications that illustrate the use of FST to study cosolvent effects on proteins and their implications for protein folding With the application of FST to study biological systems now well established, and given the continuing developments in computer hardware and software increasing the range of potential applications, FST provides a rigorous and useful approach for understanding a wide array of solution properties This book outlines those approaches, and their advantages, across a range of disciplines, elucidating this robust, practical theory K14345 ISBN: 978-1-4398-9922-9 90000 781439 899229 ... general concepts and theoretical basis of FST, and to provide a range of applications relevant to the areas of chemistry, chemical engineering, and biophysics, as described by experts in each field... and only two of those four contain the important parts of the theory It does this by giving only definitions and results and leaving the reader to fill in all of the intermediate steps Most of. .. Laboratory Department of Chemistry University of York Heslington, York, United Kingdom Ivan L Shulgin Department of Chemical and Biological Engineering State University of New York at Buffalo